2006-04
Reserve Bank of Australia
RESEARCH
DISCUSSION
PAPER
Measuring Housing
Price Growth – Using
Stratification to Improve
Median-based Measures
Nalini Prasad and
Anthony Richards
RDP 2006-04
Reserve Bank of Australia
Economic Research Department
MEASURING HOUSING PRICE GROWTH –
USING STRATIFICATION TO IMPROVE
MEDIAN-BASED MEASURES
Nalini Prasad and Anthony Richards
Research Discussion Paper
2006-04
May 2006
Economic Group
Reserve Bank of Australia
The authors thank Luci Ellis, James Hansen, James Holloway, Christopher Kent,
Kristoffer Nimark and participants at an internal RBA seminar for helpful
comments, and Australian Property Monitors for compiling the raw data used in
this paper. The views expressed in this paper are those of the authors and should
not be attributed to the Reserve Bank.
Authors: prasadn@rba.gov.au, richardsa@rba.gov.au
Economic Publications: ecpubs@rba.gov.au
Abstract
Developments in housing prices are of interest to households, policy-makers and
those involved in the housing industry. This has been the case both in Australia
and in other countries where house price developments are having significant
macroeconomic impacts. However, the construction of measures of city-wide or
nationwide average housing prices is not a straightforward exercise. One problem
is that the sample of dwellings transacted in any period may be far from random
and the characteristics of the sample may change from period to period. As a
result, widely used measures of growth in mean or median housing prices will
reflect changes in the composition of dwellings sold as well as changes in demand
and supply conditions. We demonstrate that median price measures in most major
Australian capitals are significantly affected by such compositional change.
In this paper, we propose a simple measure of house price growth that addresses
the problem of compositional change by stratifying individual transactions into
different groups. Our measure differs from those commonly used internationally in
that we group small geographic regions (suburbs) according to the long-term
average price level of dwellings in those regions, rather than just clustering smaller
geographic regions into larger geographic regions. This produces a measure of
price growth that substantially improves upon median price measures, and one that
is highly correlated with more sophisticated (but more computationally intensive)
measures. While we focus on providing a basic framework for measuring house
price growth, the stratification techniques contained in this paper have broader
applications for dealing with datasets that are affected by compositional change.
JEL Classification Numbers: G12, R31
Keywords: housing, house prices
i
Table of Contents
1.
Introduction
1
2.
The Impact of Compositional Change on Median Price Measures
3
2.1
Australian Evidence
4
2.2
International Evidence
10
3.
Stratification
11
4.
A Measure of Average Price Changes which Controls for
Compositional Changes
13
4.1
Data and Method of Stratification
13
4.2
Calculation of City-wide Quarterly Price Changes
15
5.
6.
Assessing the Mix-adjusted Median
16
5.1
Volatility
17
5.2
Seasonality
19
5.3
Revisions
20
5.4
Comparison with Regression-based Measures
21
5.5
Why Does the Mix-adjusted Measure Perform Well?
23
Conclusion
26
Appendix A: Using the Information in Individual Strata – Assessing the
Strength of Intra- versus Inter-state Influences
28
References
31
Copyright and Disclaimer Notices
ii
MEASURING HOUSING PRICE GROWTH –
USING STRATIFICATION TO IMPROVE
MEDIAN-BASED MEASURES
Nalini Prasad and Anthony Richards
1.
Introduction
Developments in housing prices are of great interest to households, policy-makers
and those involved in the housing industry. This has been the case both in Australia
and in other countries where house price developments are having significant
macroeconomic impacts. However, the construction of aggregate measures of
housing prices is not a straightforward exercise, and involves addressing a number
of conceptual and practical issues. This paper aims to provide a computationally
simple method of addressing some of these issues. While the focus of this paper is
on measuring house price growth in Australia, the method outlined in this paper
would also be feasible and readily adaptable for data from other countries.
One major problem in measuring housing price growth results from the
infrequency of transactions and the heterogeneous nature of the housing stock. To
be meaningful, price data should be based on transactions prices rather than
valuations. But only a relatively small fraction of the housing stock is transacted in
any period: in Australia the average turnover is around 6 per cent per year, or just
1½ per cent per quarter, and in other countries the turnover rate is often
significantly lower. Given that the sample of transactions in any period may not be
representative of the entire housing stock, changes in simple median or mean price
measures may not provide good estimates of the pure price change, as they will
also reflect compositional effects. In addition, problems associated with
compositional change can be exacerbated by problems of data timeliness if there is
a systematic lag between when particular sales are agreed to and when they are
recorded in a database of transactions. Hence, early estimates of changes in
housing prices may be quite unreliable, making it difficult to distinguish in real
time between true movements in the housing market from spurious movements due
to compositional effects.
2
If detailed and timely data on transactions are available, it is possible to use
regression-based approaches to deal with the problems discussed above. For
example, hedonic price regressions and repeat sales regressions can be used to
abstract from compositional effects to derive estimates of pure price changes. 1
However, many of the housing price series produced internationally do not use
such techniques but rely on simple measures such as median or mean sales prices.
For example, the Real Estate Institute of Australia, the US National Association of
Realtors, the Canadian Real Estate Organisation and the Real Estate Institute of
New Zealand (REINZ) all publish house price data which are simple median or
mean measures. The reason is presumably that the more advanced techniques
require detailed data, are typically subject to revision as data for future periods
become available, are less transparent, and require the use of statistical techniques
that are not as widely used by organisations such as industry bodies.
We show that compositional change can have major impacts on estimates of price
changes that are based on simple median measures. Accordingly, we outline and
test a simple method for calculating changes in aggregate housing prices that
controls for compositional change and which remains robust even when the initial
sample of transactions is fairly small. In particular, we propose a method that
stratifies individual house sales into different groups so as to minimise the impact
of compositional change, and then uses the median prices from those groups to
derive an estimate of the overall change in prices. We therefore demonstrate that
median prices can be considerably more useful if taken from a stratified data
sample compared with a single (unstratified) median taken from the entire data
sample.
The particular innovation of the paper is the method of stratification. A standard
method of stratification is to divide a city into broad geographical regions.
However, changes in regional composition do not necessarily result in problems
for median measures; compositional change will only be a significant problem if it
results in changes in the proportion of high- and low-priced properties.
Accordingly, we group small geographical regions (suburbs) into different strata
based on the long-term average price level of houses in those regions, thereby
directly addressing the main problem of compositional change. We find that
1 See Case and Shiller (1987), Meese and Wallace (1997) and Hansen (2006) for further
discussion of these methodologies.
3
stratifying sales in this manner produces a measure of price growth that is a
considerable improvement over an unstratified median; our measure is
significantly less noisy than a median and performs better in real time with limited
data samples. As the aim of the paper is to look at computationally simple methods
of calculating price growth, regression-based techniques are not considered,
however, Hansen (2006) provides a complementary analysis using regression
techniques. We find that the growth rates produced by our measure line up closely
with the more advanced measures contained in Hansen. This leads us to conclude
that it is possible to come up with estimates of overall changes in house prices that
are very similar to regression-based measures, but are based on simple medians
from stratification.
The rest of the paper is organised as follows. In Section 2 we present some data on
median house prices and document the strong impact of compositional change. In
Section 3, we outline how stratification techniques – a method commonly used in
other contexts – can control for compositional change. Section 4 outlines our
method of controlling for compositional change, while Section 5 provides an
assessment of the resulting measure of housing prices. Section 6 concludes.
2.
The Impact of Compositional Change on Median Price
Measures
Median or mean house price series are produced in many countries. 2 One clear
advantage of median price measures is that they are very easy to calculate. They
also have a straightforward interpretation: they represent the price in a ‘typical’
transaction in any given period.
However, if one is interested in inferring the price change for the overall housing
stock, these measures can be distorted by compositional change. In particular, the
transactions that occur in any period may not be representative of the overall
2 In Australia, the price data produced by the Real Estate Institute of Australia and the
Commonwealth Bank are simple unstratified medians (with no allowance for possible
seasonality). In addition to the measures already mentioned, many house price measures in
continental Europe also use a mean or median to measure prices, for example, measures
constructed in Belgium, Denmark, Ireland, Luxembourg, Norway and Switzerland.
4
housing stock. Or more importantly for estimating price changes, the composition
of the sample of transactions in one period may be quite different to the
composition in the next period. As a result, changes in median and mean prices
may contain substantial noise from compositional change and provide poor
estimates of price changes that result from changes in demand and supply
conditions.
2.1
Australian Evidence
We can illustrate the problems resulting from compositional change using
quarterly data for median prices of houses transacted in Sydney between
March quarter 1993 and September quarter 2005. The top panel of Figure 1 shows
the quarterly median price (on a log scale). The middle panel shows the quarterly
change in this series along with a line for the trend quarterly growth. 3 ,4 These
series indicate that there was substantial growth in median prices over most of this
period, but with substantial noise, which is apparent in the sometimes large
divergences between the actual and trend change in the median.
In the bottom panel of Figure 1, we introduce a measure of compositional change
which may be able to explain some of the noise in the median price. To construct
this variable, the 659 suburbs in Sydney were ranked according to their median
transaction prices over 2000–2004, and then allocated into 10 groups (or deciles),
with an approximately equal number of suburbs in each group. Decile 1 consists of
the 65 suburbs with the lowest median prices, while Decile 10 consists of the
66 suburbs with the highest median prices. For each quarter, we then calculate the
proportion of transactions in the more expensive suburbs (Deciles 6–10). In the
case of Sydney, this proportion averages somewhat below 50 per cent because the
allocation of suburbs was done to ensure a similar number of suburbs, rather than
3 Through the rest of the paper, all calculations involving changes in prices use the change in
the log of the price series. In cases where we show these in a table, they are the log change
multiplied by 100 so as to correspond approximately to percentage changes.
4 The trend is calculated as the change in the five-quarter-centred moving average of (the log
of) the median price series. The weights in the moving average are 0.125, 0.25, 0.25, 0.25,
and 0.125, which should remove any seasonality from the trend.
5
Figure 1: Median House Prices
Sydney, nsa
$’000
$’000
Median prices, log scale
445
445
345
345
270
270
210
210
%
10
%
10
Growth in median prices
Trend
5
5
0
0
-5
-5
Quarterly growth
%
55
Proportion of sales in more expensive suburbs
50
50
45
45
40
40
35
35
1993
Source:
%
55
1996
1999
2002
2005
Authors’ analysis using data from APM
transactions, in each decile. 5 The data show that there is significant quarterly
variation in the proportion of transactions in the more expensive suburbs of
Sydney. 6 This leads to noise in the median measure, as measured price growth
reflects both changes that result from compositional effects as well as pure price
changes. An illustration of the noise in quarterly growth of the city-wide median
measure is that, in most cases, quarterly growth in this series is outside the range of
the middle six decile growth rates. Indeed, in nearly half of all quarters in the data
5 All the raw data used in this paper, including the division of data into deciles, has been
provided by Australian Property Monitors (APM). The results in Sections 5.3 and 5.5 are
based on unit record data provided by APM.
6 It is interesting that there also appears to be a downward trend in this ratio over most of the
sample, perhaps because the growth in the city has been in suburbs relatively far from the
centre, which tend to be less expensive suburbs. This suggests that measures of median prices
might understate true longer-run price growth over the entire period. We do not address this
issue, but instead focus on improving estimates of short-run changes in house prices.
6
sample, the quarterly changes in the city-wide median is actually outside the range
of median price changes in all ten deciles (Figure 2).
Figure 2: Median House Price Growth and Compositional Change
Sydney, nsa
%
%
Median house price growth
■ Range of the middle six decile growth rates
■ Range of all decile growth rates
●
10
●
10
●
●
●
●
●
5
●
●
0
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
0
●
●
●
-5
●
●●
●
●
●
●
●
●
●
5
●
●
●●
●●
●
●
●
-5
●
●
●
●
-10
-15 l
1993
Source:
l
l
l
l
1996
l
l
1999
-10
l
l
l
l
2002
l
-15
2005
Authors’ analysis using data from APM
We can formally test the proposition that compositional change between higherand lower-priced suburbs may be responsible for some of the observed noise in the
change in median house prices. We regress quarterly changes in median prices on a
constant and a compositional change variable, given by the quarterly change in the
proportion of dwellings sold in more expensive suburbs. We estimate this equation
using data from June quarter 1993 to September quarter 2005 for median house
prices in the six largest cities (Sydney, Melbourne, Brisbane, Perth, Adelaide and
Canberra). 7 We also estimate it for apartment prices in Sydney and Melbourne,
which account for around 70 per cent of the stock of capital-city apartments. In
most cases we proxy the proportion of house sales in more expensive suburbs by
sales in the top five deciles. The exception is the house market in Canberra and the
apartment market in Sydney and Melbourne. Given the smaller size of these
markets, transactions were grouped into five groups (quintiles), and we classify the
7 Houses are defined to include both detached and semi-detached dwellings.
7
middle quintile in such a way as to have an approximately equal number of sales in
the higher- and lower-priced segments.
Results are shown in Table 1. In all cases the compositional change variable takes
the expected positive sign: an increase in the proportion of transactions in higherpriced suburbs leads to the change in the median price being higher. 8 For Sydney
and Melbourne, the results indicate that a considerable proportion – around
60 per cent – of the quarterly variation in median house prices can be explained
purely by shifts in the mix of sales between higher- and lower-priced suburbs. The
effect of compositional change is notable, though less pronounced in the other
markets, explaining around 20 to 40 per cent of quarterly price movements. The
exception is Brisbane which appears to be much less affected by this form of
compositional change. Overall, the results in Table 1 suggest fairly strongly that
there may be significant gains from taking account of the effect of this simple form
of compositional change on median price measures.
Table 1: Testing for the Impact of Compositional Change on Median Prices
Regression results
Sydney houses
Melbourne houses
Brisbane houses
Perth houses
Adelaide houses
Canberra houses
Sydney apartments
Melbourne apartments
Notes:
Coefficient on compositional
change variable
Adjusted R2
1.09***
0.77***
0.56*
0.70***
0.89***
0.45***
0.70***
0.92***
0.60
0.63
0.05
0.20
0.26
0.18
0.37
0.39
This table shows results from a regression to determine if the quarterly growth in median house prices
over 1993:Q2–2005:Q3 is affected by changes in the composition of dwellings sold. The regression
estimated is Δpt=α+β∆comt + εt where Δpt is the quarterly change in median prices, ∆comt is the quarterly
change in the proportion of transactions in more expensive suburbs, and εt is the error term. Significance
at the 1, 5 and 10 per cent levels is denoted by ***, ** and *, respectively.
8 We have also regressed the compositional change variable on our stratified measure of price
changes, which account for compositional change. The results indicate that there is no
tendency for the compositional change variable to be related to true changes in house prices,
so the results in Table 1 reflect spurious compositional effects on median prices.
8
A close look at Figure 1 suggests that part of the quarterly variation in the
composition of dwellings sold may be seasonal in nature. Accordingly, we test for
identifiable seasonality in the composition of sales and in the level of prices using
the US Census Bureau’s X12 seasonal adjustment program. In addition, we regress
the quarterly change in the proportion of dwellings sold in more expensive suburbs
and the quarterly change in the median price on seasonal dummies. While X12
provides a more sophisticated approach to testing for seasonality (by
differentiating between trend, cyclical and seasonal influences and allowing
seasonal patterns to vary over time), the adjusted R2 from the seasonal dummy
variable regressions provides a straightforward way of comparing the importance
of seasonality in different series.
Panel A of Table 2 contains results from testing for seasonality in the proportion of
houses sold in more expensive suburbs and Panel B contains the results for median
prices. Both median prices and the composition of transactions are found to be
seasonal in most capital cities. Furthermore, cities where the composition of
transactions is found to exhibit a seasonal pattern tend to be the ones where median
prices are found to be seasonal, suggesting that at least part of the seasonality seen
in median prices is the result of seasonality in the composition of sales. 9 The sign
and size of the seasonal factors on the compositional change and median price also
support this, with the quarters when median prices are seasonally high (typically
the December quarter in most cities) tending to be the quarters when the proportion
of sales in higher-priced suburbs is also seasonally high. The values for the
adjusted R2 suggest that seasonal influences are particularly strong in the market
for houses in the two largest capitals, explaining as much as a third (Sydney) or
half (Melbourne) of the variation in quarterly price movements. Given that there is
significant seasonality in most capital cities, and that the pattern of seasonality in
the two largest cities is very similar, it is not surprising that there is also
seasonality in average nationwide prices (which are calculated as the weighted
average of prices in each capital city market using dwelling stock weights).
Seasonal factors can explain nearly 40 per cent of quarterly price movements at the
national level.
9 It is beyond the scope of this paper to consider the reasons for the seasonality in the
composition of sales. However, it is interesting that in each of the capital cities where sales
volumes are found to be most seasonal, the seasonality comes more from variation in the sales
volumes in higher-priced suburbs than in lower-priced suburbs. This would be consistent with
some cities having particular ‘selling seasons’, especially in higher-priced suburbs.
9
Table 2: Testing for Seasonality
Is identifiable
seasonality present
in X12?
Adjusted R2 from regression of
quarterly change in the dependent
variable on seasonal dummy variables
Panel A: Testing for seasonality in the compositional change variable
Sydney houses
Yes
0.60
Melbourne houses
Yes
0.83
Brisbane houses
No
0.14
Perth houses
Yes
0.29
Adelaide houses
Yes
0.47
Canberra houses
No
0.05
Sydney apartments
Yes
0.53
Melbourne apartments
Yes
0.31
Panel B: Testing for seasonality in median house prices
Sydney houses
Yes
0.33
Melbourne houses
Yes
0.50
Brisbane houses
No
0.02
Perth houses
Yes
0.14
Adelaide houses
Yes
0.26
Canberra houses
No
–0.02
Sydney apartments
Yes
0.26
Melbourne apartments
No
0.09
Australian housing
Yes
0.39
Panel C: Testing for seasonality in selected international median and mean price series
US
Northeast
Yes
0.23
Midwest
Yes
0.45
South
Yes
0.55
West
Yes
0.18
United States nationwide
No
–0.02
Canada
Toronto
Yes
0.29
Canada nationwide
Yes
0.11
NZ
Auckland
No
0.02
Waikato/Bay of Plenty
Yes
0.11
Wellington
Yes
0.55
Yes
0.09
Canterbury/Westland
New Zealand nationwide
Yes
0.11
Note:
The Australian sample covers 1993:Q1–2005:Q3; the overseas data covers varying periods (see
Footnote 10).
10
However, the relationship between changes in median prices and changes in the
proportion of houses sold in more expensive suburbs is not purely due to common
seasonality. For each capital-city market, we have also regressed quarterly changes
in seasonally adjusted median prices on a constant and the seasonally adjusted
compositional change variable. The adjusted R2s from these regressions are lower
than those in Table 1. However, in nearly all cities (the exceptions are Brisbane
and Adelaide) the seasonally adjusted compositional change variable can explain a
notable amount of the quarterly change in the seasonally adjusted median price,
with adjusted R2s ranging from between 0.10 (for Perth houses) to 0.37 (for
Melbourne apartments). Therefore, there also exist significant non-seasonal shifts
in the proportion of sales in more and less expensive suburbs that will be reflected
in movements in median prices.
2.2
International Evidence
We have not been able to do similarly detailed tests of the impact of compositional
change on median prices for other countries due to the absence of similar time
series data for the share of transactions in different segments of the market.
However, in Panel C of Table 2 we apply similar tests for seasonality to some
readily available international housing price series. These are the median series
produced by the US National Association of Realtors and by the Real Estate
Institute of New Zealand (only major regions are shown) and the mean series from
the Real Estate Institute of Canada. 10 The results are comparable to Australian
data, with median and mean prices in nearly all regions found to be seasonal. In
some cases, seasonal dummies alone are able to explain a significant proportion of
the quarterly variation in prices.
We can think of no compelling reason as to why pure house price changes should
be seasonal. Accordingly, the results suggest that price measures in these countries
are also being significantly affected by compositional change, consistent with
observations made by others (for example, McCarthy and Peach 2004, p3 and
REINZ 2005). It therefore appears that the problem that we address in this paper
10 The series for the US, Canada and New Zealand refer to existing one-family homes,
dwellings, and existing dwellings, respectively. The analysis uses data for 1975:Q2–2005:Q4
for the US, 1980:Q1–2005:Q4 for Canada and 1992:Q1–2005:Q4 for New Zealand. The US
data have been converted to a quarterly series by averaging the monthly series.
11
may be a fairly general one, suggesting that the solution proposed here may also
have wider relevance for house price measures published in some other countries.
3.
Stratification
The problems illustrated in Section 2 reflect the fact that the prices recorded in any
quarter relate to only a sample and not the entire population of houses. This would
not be a significant problem if the sample was a random sample from the
population of all houses. Despite the significant number of transactions available
each quarter, the results above suggest that the observed samples in any quarter are
far from random. Given that there is no ex ante way of ensuring a random sample
of housing transactions, the issue becomes one of dealing ex post with the nonrandomness of the sample.
The measure for the change in house prices that is proposed in this paper uses mixadjustment, which in turn uses stratification, to control for compositional change.
Stratification is a commonly used technique because it can increase the precision
of sample estimates (Hansen, Hurwitz and Madow 1953). Indeed, it is a method
employed in measuring house prices in a number of countries (Table 3). 11
However, as is discussed in more detail below, the method that we use to stratify
our sample differs significantly from most other applications in one respect.
Stratification involves dividing a population into groups (strata) such that
observations within each group are more homogenous than observations in the
entire population. Within each stratum, it then becomes more likely that an
observed change in a characteristic of interest represents a true change rather than a
spurious one due to compositional effects. Once strata have been defined, a
measure of central tendency from each strata is weighted together to produce an
aggregate price measure.
11 See ABS (2005, pp 6–8) for some additional discussion of the use of stratification in house
price measurement.
12
Table 3: Mix-adjusted House Price Measures in Selected Countries
Index provider
Variables used in mix adjustment
Australian Bureau of
Statistics (ABS)
Hong Kong Monetary
Authority
Urban Redevelopment
Authority (Singapore)
Bank of Canada/
Royal Le Page
Deutsche Bundesbank/
Bulwien AG
Ministerio de Formento
(Spain)
Region, percentage of three-bedroom houses within a region and
an index of the social and economic conditions in a suburb
The saleable area of a dwelling
Hometrack (UK)
Rightmove (UK)
Office of the Deputy Prime
Minister (ODPM, UK)
Dwelling type and region, with prices quoted in per square metre
terms
Region and dwelling type
Region and dwelling type
Calculates the average price of a house per square metre.
Distinguishes between dwellings based on location and size of
municipalities
Postcode and dwelling type
Postcode and dwelling type
Region, locations within region, dwelling type, old or new
dwelling and first or repeat-home buyer purchase. A hedonic
equation is used to calculate the price for each strata.
Sources: ABS (2005); BIS database; various national sources
Traditionally, the variable which has been used to group transactions is geography
(Table 3). 12 Defining housing strata based on geography captures the notion that
dwellings in a given area share amenities linked to the property’s location. In
addition, the literature on housing submarkets finds that geographic variables are
an important determinant of housing prices (see Bourassa et al 1999 and
Goodman and Thibodeau 2003). Similarly, work using Australian data by the
ABS (2005) and Hansen (2006) finds that location is a fundamental pricedetermining characteristic of dwellings. Another reason for grouping by location is
a practical one; geographic variables are readily available in most databases of
housing transactions (Goodman and Thibodeau 2003).
12 In addition to location, most measures which use stratification also group transactions
according to dwelling type. As well as the measures in the table, a number of countries in
continental Europe (including Austria, Finland, Hungary and Portugal) make a rudimentary
adjustment for quality by measuring prices in per square metre terms. Beyond this, most
measures do not control for quality. This is probably because very few datasets contain
comprehensive information on dwelling characteristics.
13
The increase in precision gained from stratification is dependent on how strata are
defined. Hansen et al (1953) suggest that strata boundaries should be defined using
information on all relevant variables that influence the characteristic being
measured. Similarly, Lavallée (1988) notes that the most useful variables for
stratifying data are those that are highly correlated with the variable of interest.
In the current case, we are particularly concerned about removing the noise in
changes in median prices that results from the combination of compositional
change and the extreme range in housing prices (the fact that prices of some houses
in a city may be more than 10 times higher than the prices of other houses). For our
exercise we have no particular interest in trends in house prices across different
regions of a city. Furthermore, purely geographical stratification is unlikely to
divide houses into strata with the maximal feasible similarity in prices within
strata. Accordingly, we group houses and suburbs into strata based on the variable
that is most likely on an a priori basis to explain the price in any transaction,
namely the long-term level of prices for the suburb where the house is located.
4.
A Measure of Average Price Changes which Controls for
Compositional Changes
Based on the discussion in Sections 2 and 3, we propose a measure of changes in
average housing prices that controls for one important form of compositional
change. We refer to this hereafter as the change in the mix-adjusted measure.
4.1
Data and Method of Stratification
Our measure uses data for March quarter 1993 to September quarter 2005,
prepared by APM. The dataset provided by APM contains virtually the entire
population of housing transactions that occurred over this period.
As a starting point, transactions were grouped together by location, based on the
suburb where the property is located. 13 However, because a city like Sydney has in
excess of 600 suburbs, this would be too great a level of disaggregation to be
13 The use of suburbs rather than postcodes allows a greater degree of disaggregation as
postcodes often incorporate more than one suburb.
14
practical if simplicity of calculation is one of the key considerations for a simple
mix-adjusted measure. Further, it is likely that during some quarters the number of
sales within a suburb may be quite small (or zero), hindering the estimation of a
price movement for that suburb. Therefore an additional criterion is required to
cluster together individual suburbs and hence reduce the number of strata.
For simplicity, median sale prices in each suburb over the period 2000–2004 were
used to group suburbs into strata. For the house price data, suburbs in the
five largest cities were grouped into deciles, each with an approximately equal
number of suburbs, based on median prices over 2000–2004. For example, of
the 446 suburbs in Melbourne, the first stratum for Melbourne consists of the
44 suburbs with the lowest median prices, while the tenth stratum consists of the
45 suburbs with the highest median prices. In the case of house prices for Canberra
and apartment prices for Sydney and Melbourne, there are fewer transactions, so
we group them into quintiles of equal number of suburbs.
There would, of course, be many other ranking periods that we could use for
grouping suburbs into strata based on median prices. For example, we could use
the median price of suburbs in 1992 to form strata for 1993, then the median prices
for 1993 to form strata for 1994, and so on. However, in practice there is a very
high degree of stability in the relative price rankings of suburbs: suburbs that tend
to be relatively expensive in one period will tend to be relatively expensive 10
years later. Figure 3 illustrates this using data for Sydney, showing that the price
relativities in the 2000–2004 sorting period also hold outside that period. 14 The
same result holds almost without exception for all cities and for both houses and
apartments. Hence, any reasonable alternative price-based strategy for ranking
suburbs would result in very similar strata, and very similar estimates of price
growth.
14 The Spearman rank correlation between median suburb prices in Sydney in 1996 and 2004 is
0.95, which confirms that suburbs tend to maintain their relative price rankings.
15
Figure 3: Median Decile Prices
Sydney houses, log scale, nsa
$’000
$’000
1 205
1 205
440
440
165
165
60
1993
1996
1999
2002
2005
60
Notes:
The lines represent the median price for each of the 10 deciles in Sydney. The shaded area shows the
period used to sort the data.
Source:
Authors’ analysis using data from APM
4.2
Calculation of City-wide Quarterly Price Changes
Once suburbs were grouped into deciles (or quintiles), a median price was
calculated for each strata for each quarter. The change in the median prices for
each strata were then weighted together to calculate growth in city-wide prices.
There are a number of different weighting schemes that could be used to combine
these ten (or five) growth rates. The simplest method would be to take an
unweighted average of the changes. This is equivalent to constructing a city-wide
index as the unweighted geometric average of median prices in each strata.
Alternatively, we have also investigated the effect of using weights based on sales
volumes over the 12-year period, and weights based on principal components
16
(where changes in prices for any group can be thought as given by an unobservable
city-wide movement plus an idiosyncratic component). 15
However, different weighting schemes make very little difference to estimates of
short-term price growth. In our sample, the different weightings yield measures of
quarterly price changes which typically have a correlation of over 0.99. This
reflects the fact that price changes in the different strata are typically reasonably
highly correlated (see Appendix A). Nevertheless, in most cases, sales volumes
and principal components imply weights for each stratum that are close to equal
weights. Given that equal-weighting produces similar results to other weighting
schemes and given that it is the simplest method of weighting the series, all the
results shown in subsequent sections of this paper refer to the equally-weighted
measure (which is labelled as the ‘mix-adjusted measure’).
5.
Assessing the Mix-adjusted Median
We assess our alternative measure of changes in city-wide house prices by
examining how well it addresses the problems with conventional unstratified
median measures that were highlighted in Section 2. An additional benchmark is
whether our measures outperform the change in the seasonally adjusted median
price: this will indicate if the slightly greater data demands of our measure yields a
significant improvement relative to a simple alternative approach to dealing with
the problem of seasonality and compositional change. In addition, we also compare
the correlation of our measure with regression-based measures. We then provide
some additional perspective on the reasons for the good performance of our simple
measure.
15 If the intention is to measure changes in the value of the housing stock, the most appropriate
weighting would be to use suburb-level dwelling stock weights. Data limitations prevented
this for the current exercise, but the results are likely to be little different to the results
presented here, especially for short-term price movements.
17
5.1
Volatility
Price movements that result from compositional effects can be considered as
representing noise that adds volatility to quarterly price changes rather than being
indicative of true trends in the housing market. Indeed, the results in Panel A of
Table 4 indicate that quarterly changes in median housing prices in Australian
cities are highly volatile. 16 In every case, simply seasonally adjusting the median
price series (using the X12 program) results in a measure of price changes that is
considerably less volatile than the change in the unadjusted median. However, in
every case there is an additional improvement that can be gained from our simple
mix-adjusted measure.
The reduction in volatility between the non-seasonally adjusted median and the
mix-adjusted measure is greatest for Sydney and Melbourne houses, where the
standard deviation is reduced by half. Indeed, it is noteworthy for Sydney and
Melbourne houses that the standard deviation of price changes in every one of the
ten deciles is noticeably smaller than the standard deviation of the change in the
median for the entire city. To be provocative, these results for Sydney and
Melbourne suggest that one might get better estimates of the trend in city-wide
house prices by looking at developments in a sample of only about 10 per cent of
all sales (albeit a carefully selected 10 per cent) than from a standard median
measure using the full sample of data.
The comparisons in Panel A of Table 4 implicitly assume that the amount of
‘noise’ in a series for price changes can be proxied by its standard deviation, that
is, by the variability relative to the average change over the entire sample period.
An alternative would be to recognise that there are cycles in price movements, so
we should assess different series for price changes based on how closely they
match a measure of the ‘trend’ change in prices. Accordingly, we construct a
moving-average measure of the trend change in prices for each city. For each price
measure we then calculate a root mean squared error (RMSE) between quarterly
16 McCarthy and Peach (2004) find that US median prices are also volatile. Indeed, the growth
rate in the nationwide median price series produced by the National Association of Realtors is
2½ times more volatile than the growth in the repeat-sales index produced by the Office of
Federal Housing Enterprise Oversight.
18
growth in the measure and quarterly growth in the trend. 17 Since the trend measure
can be thought of as capturing underlying housing price movements, the larger the
deviations from trend, the less informative the series is about the underlying state
of the housing market.
The results for the RMSE in Panel B of Table 4 again suggest that a seasonally
adjusted median price series offers an improvement over the standard median, but
that the mix-adjusted measure provides a more significant improvement for all
capital cities. Taking the reduction in the Australia-wide measure as a simple
metric for the reduction in the proportion of noise in the standard median, one
might conclude that seasonal adjustment can typically reduce the extent of noise by
nearly 40 per cent, but that the mix-adjusted measure results in a more significant
reduction, with the average volatility falling by nearly 70 per cent.
The reduction in volatility from adjusting for compositional change appears to be
significantly greater for houses in Sydney and Melbourne than in the other capitals.
The gains from stratification will depend on several factors including: the extent of
compositional change between higher- and lower-priced properties in each city; the
extent of price differences between higher- and lower-priced properties; and the
extent to which we can ‘undo’ the effects of compositional change via the suburblevel stratification strategy used here. We cannot be definitive about the reasons for
the relatively larger gains for the larger cities, but they appear to reflect both a
higher degree of compositional change in these two cities (including the seasonal
component shown in Panel A of Table 2), and greater variation in the
characteristics of the dwelling stock in Sydney and Melbourne (for example, the
median house price for the tenth decile in Sydney is on average 2.7 times higher
than the city-wide median, compared with around 2.2 times higher for most of the
other capitals). In addition, since the largest cities have the largest number of
suburbs (for example, 659 for Sydney versus 313 for a medium-sized city like
Perth), it is possible to divide larger cities into more differentiated strata with
17 The trend is calculated using the moving-average approach described in Footnote 4. We first
construct two measures of trend, one from an index version of our mix-adjusted measure and
the other using the seasonally adjusted median. The measure of trend used in the comparisons
in Table 4 is the average of the two measures: we do this to ensure a fair ‘horse-race’ between
our measure and the seasonally adjusted measure (though the results are not sensitive to the
assumptions about the calculation of the trend).
19
greater variation in the average prices of suburbs in each strata. Hence it would be
expected that there would be greater gains from stratification and greater control of
compositional change in the larger cities.
Table 4: Volatility in Measures of Changes in Housing Prices
Per cent
Median
(nsa)
Median
(sa)
Mix-adjusted
measure
Range for deciles/
quintiles (nsa)
Panel A: Standard deviation of quarterly changes
Sydney houses
Melbourne houses
Brisbane houses
Perth houses
Adelaide houses
Canberra houses
Sydney apartments
Melbourne apartments
4.35
4.62
3.10
2.29
2.90
3.51
2.27
3.87
3.30
3.00
2.92
1.98
2.36
3.44
1.87
3.50
2.16
2.26
2.92
1.80
2.27
3.06
1.84
2.70
Australian housing
3.13
2.25
1.81
2.36–3.61
2.24–3.86
2.92–5.21
2.46–3.62
2.73–6.17
3.57–5.12
2.17–3.18
3.36–5.73
Panel B: Deviation from trend (quarterly RMSE)
Sydney houses
Melbourne houses
Brisbane houses
Perth houses
Adelaide houses
Canberra houses
Sydney apartments
Melbourne apartments
4.04
4.40
1.91
1.90
2.20
2.46
1.93
3.45
2.80
2.54
1.61
1.49
1.37
2.41
1.46
3.01
1.08
1.40
1.26
1.07
1.27
1.88
1.21
2.11
Australian housing
2.81
1.73
0.88
Note:
The sample covers 1993:Q2–2005:Q3.
5.2
Seasonality
1.41–2.99
1.36–3.48
1.73–4.88
1.73–3.10
1.71–6.07
2.33–4.78
1.60–2.89
2.78–5.59
By construction, our mix-adjusted measure will remove any impact on measures of
price changes that results from seasonality in the composition of sales across
strata. However, it will not control for any seasonality from compositional effects
within strata. To see if seasonality within strata is an issue, we have tested our
20
measure for the presence of any residual seasonality. While median prices in nearly
all capital cities were found to be seasonal, the results (available upon request)
indicate that mix-adjusted changes are not seasonal in any capital city, nor at the
nationwide level.
Therefore, by controlling for one form of compositional effect through
stratification, we are providing a control for the seasonality that is apparent in
median measures. In addition to this, it appears that we are also controlling for
some degree of non-seasonal compositional change. Accordingly, our measure
appears in Table 4 to be a significant improvement over the seasonally adjusted
measure.
5.3
Revisions
An additional test of the mix-adjusted methodology is the extent to which it
performs well in real time, as opposed to the previous comparisons in this paper
which are based on more final data. The real-time data problem is the result of the
decentralised nature of the housing market in Australia, which means that
information on house prices has often used data from state land titles offices
reported only after the settlement of transactions. This means that sales information
is often not available until several months after the agreement on the transaction
price. Therefore, initial estimates of prices in transactions occurring in any given
quarter may be based on only a small sample of all transactions that will eventually
be available.
If there are systematic differences in the lag between agreement on a sale and the
reporting of the sale, early samples of transactions may be quite unrepresentative
of the final population of sales. For example, a simple median will be biased
downwards if more expensive houses are under-represented in initial samples.
Hence, early estimates of changes in housing prices may be unreliable, making it
difficult to discern true movements in the housing market from those that result
from small sample size or compositional effects. Indeed, the pattern of upward
revisions to real-time estimates of median house prices in most Australian capitals
21
suggest that lower-priced houses are over-represented in initial samples of
transactions. 18
To examine potential problems with early estimates, we use data on individual
sales in Sydney, provided by APM, to estimate ‘real-time’ city-wide price growth.
We calculate an ‘initial’ estimate of house price growth using data available one
month after the end of each quarter and compare this with ‘final’ estimates
calculated from the latest available vintage of data; this corresponds to an initial
sample that is typically less than half the size of the final sample. 19 A RMSE is
then calculated between the ‘initial’ and ‘final’ estimate of price growth for each
measure. The results show that the standard median is subject to considerably
greater revision (a RMSE of around 7½ percentage points) than the mix-adjusted
measure (a RMSE of about 1½ percentage points). Hence, our technique of
stratification appears to offer an even greater improvement over a simple median in
real time. The improved real-time performance of the mix-adjusted measure is not
entirely surprising given that one of the rationales for stratification is that it can
reduce the size of a sample required to produce reliable statistics (Briggs and
Duoba 2000).
5.4
Comparison with Regression-based Measures
One clear advantage of a mix-adjusted measure is its relative simplicity. However,
more sophisticated approaches are possible, most notably the two regression-based
measures studied in Hansen (2006). Of course, these approaches are not without
shortcomings. For example, hedonic regressions will only be as good as the data on
housing characteristics that are available. Repeat-sales estimates are likely to have
significant problems in real time and can be subject to non-trivial revisions, given
18 We will not focus on the question of why there appears to be some correlation between the
sale price of houses and the time taken for settlement, reporting and recording of transactions.
However, possible explanations would be that settlement conventions tend to be longer in
more expensive areas (this could be because buyers of more expensive houses are more likely
to be repeat-home buyers who may want a longer settlement period so that they can finalise
selling their previous dwelling), that such buyers may tend to perceive benefits from delaying
reporting their transactions, or that the processing of title changes in older (more expensive)
suburbs might take longer than those in newer (less expensive) suburbs.
19 The individual sales data used contain sales recorded up to September quarter 2005. The
RMSEs are calculated on data for sales from the March quarter 1996 to the June quarter 2005.
22
that estimates of price growth in any quarter will be affected by sales that occur in
subsequent quarters.
In Table 5, we use correlation coefficients and a measure of deviations from trend
to compare our measure and the estimates from Hansen (2006) of quarterly price
changes for houses in the three large capitals from hedonic and repeat-sales
regressions. Panel A of Table 5 indicates that the change in the simple median
often has a fairly modest correlation with the regression-based measures. Seasonal
adjustment of the median produces quarterly growth rates that are slightly more
correlated with these measures. However, our measure of the quarterly growth in
prices is considerably more correlated with the regression-based measures. Indeed,
the mix-adjusted measure tends to have a slightly higher correlation with each of
the regression-based measures than the correlation between those more advanced
measures.
Panel B indicates the extent to which each of the measures of house price growth
deviate from a proxy of underlying house price movements. 20 Confirming the
earlier results in Table 4, changes in the median and seasonally adjusted median
are volatile with relatively high RMSEs. In contrast, our mix-adjusted measure and
the two regression-based measures provide estimates of underlying house price
movements that are comparable in terms of their apparent noise.
It is reassuring that the results from the mix-adjusted measure are similar to those
from regression-based measures, suggesting that simple stratification techniques
can control for a significant proportion of compositional change. However, it is not
especially surprising that our measure is highly correlated with the hedonic
measures. The results in Hansen (2006) indicate that the vast majority of the
explanatory power in standard hedonic regressions comes from the location of
properties, which (in combination with information on average suburb-level price
levels) is the variable used for stratification in our methodology.
20 We construct a measure of trend growth for each of the mix-adjusted, hedonic and repeat-
sales measures (using the moving-average approach outlined in Footnote 4) and then average
these three trends to obtain a proxy for underlying growth in house prices for each city.
23
Table 5: Correlation between Various House Price Measures
Median
(nsa)
Median
(sa)
Mix-adjusted
Hedonic
Repeat-sales
Panel A: Correlation coefficients, quarterly changes
Sydney
Median (nsa)
Median (sa)
Mix-adjusted median
Hedonic
Repeat-sales
Melbourne
Median (nsa)
Median (sa)
Mix-adjusted median
Hedonic
Repeat-sales
Brisbane
Median (nsa)
Median (sa)
Mix-adjusted median
Hedonic
Repeat-sales
1.00
0.77
0.52
0.58
0.38
1.00
0.65
0.65
0.57
1.00
0.97
0.90
1.00
0.89
1.00
1.00
0.69
0.65
0.66
0.42
1.00
0.71
0.70
0.57
1.00
0.92
0.76
1.00
0.69
1.00
1.00
0.95
0.87
0.89
0.77
1.00
0.87
0.90
0.81
1.00
0.96
0.93
1.00
0.93
1.00
Panel B: Deviation from trend (quarterly RMSE)
Sydney
Melbourne
Brisbane
4.11
4.48
1.96
2.95
2.64
1.69
0.97
1.40
1.25
1.02
1.25
1.25
0.86
1.57
1.03
Notes:
Correlation coefficients and RMSEs across the various measures of quarterly price growth were
calculated over 1993:Q2–2005:Q3. The data vintage used to calculate the hedonic and repeat-sales
measures in Hansen (2006) does not correspond precisely with that used to calculate the mix-adjusted
median here. In addition, Hansen uses data from a different source (Real Estate Institute of Victoria) to
calculate the repeat-sales measure for Melbourne, so the results across measures are not fully comparable
for Melbourne.
5.5
Why Does the Mix-adjusted Measure Perform Well?
The preceding analysis indicates that the mix-adjusted approach overcomes many
of the problems associated with unstratified median measures. A major reason for
the substantial improvement appears to be the particular method we have used to
24
stratify transactions. By stratifying properties on the basis of the median price for
their suburb, we are controlling for much of the compositional change in sales
movements between higher- and lower-priced properties. However, other
stratification strategies are possible, an obvious alternative being on a broad
geographical basis, which is a common strategy internationally. Accordingly, in
this section we compare the results of price-based and geographic stratification
strategies.
We use unit record data for Sydney to construct two alternative mix-adjusted
measures of price changes. Two standard geographical classifications of Sydney
are based on statistical local areas (SLA) and statistical subdivisions (SSD), of
which there are 49 and 14 groups respectively. We construct measures using both
of these geographic groupings. To produce a city-wide measure of price growth,
the median house price in each geographic region is weighted by the region’s share
of sales over the whole sample period. In order to evaluate the relative
performance of the geography-based measures of price growth, we calculate the
deviation (RMSE) of each measure from the trend growth series used in Panel B of
Table 5.
For greater comparability, we also calculate some alternative price-based mixadjusted measures. Instead of dividing Sydney into 10 price-based groups, we
divide it into 14 and 49 groups (the same number of groups as the geographic
measures) based on the median price of that suburb over 2000–2004. However, to
shed further light on the stratification issue, we implement some additional pricebased measures. In particular, instead of forming measures based just on 10, 14
and 49 strata, we assess the robustness of price-based measures using everything
from 1 stratum (equivalent to the simple city-wide median) all the way up to
60 strata (each with just 10 or 11 suburbs).
The results are shown in Figure 4. 21 A first point to note is that price changes
estimated from the geographic-based stratifications are less noisy than the simple
city-wide median. The RMSEs based on the 14 and 49 groups are 1.95 and
21 Due to some constraints in the unit record data, the results here differ somewhat from the
results in Tables 4 and 5. The measures in this section are constructed using unit record
data that are of a different vintage and cover a different time span (March quarter 1996 to
June quarter 2005) to most of the data used in the rest of the paper.
25
1.62 per cent respectively, versus 4.70 per cent for the city-wide median. However,
the price-based stratification measures provide a significant additional
improvement over the geography-based measures, with RMSEs of 1.15 and
1.14 per cent, respectively, for the measures based on 14 and 49 groups. This
provides evidence in support of grouping data on the basis of median suburb prices
rather than on a geographic basis, as the former provides a better control for
changes in the mix of sales between more and less expensive properties.
An important additional result in Figure 4 concerns the ‘granularity’ of
stratification in our price-based measures. The line on the graph shows how the
deviation from trend (as a RMSE) varies according to the number of strata used to
calculate price growth. We see that simply dividing all transactions into two groups
of about 330 suburbs produces notable gains over the median measure. There are
further significant gains from splitting the sample into four groups, but thereafter
the RMSE is fairly constant. This implies that one can get fairly comparable
estimates of movements in Sydney house prices by dividing Sydney’s 659 suburbs
into anything from 4 to 60 groups: this is also confirmed by correlation analysis.
Therefore, the results for Sydney that we have shown earlier in the paper are not
particularly sensitive to our decision to divide suburbs into 10 groups: indeed there
is a wide range of price-based stratification schemes that yield robust results.
We conjecture that the results for other cities are also not especially dependent
upon our decision to group suburbs into deciles (or quintiles). We have not aimed
to fit the suburbs in each capital city into an ‘optimal’ number of groups: the
choice of deciles was fairly arbitrary on our part, though in cases of smaller sample
sizes (houses in Canberra, and apartments in Sydney and Melbourne) we decided
to instead work with quintiles to avoid small sample sizes in particular strata,
especially in the incomplete real-time samples. For other applications, there will no
doubt be benefits to empirically testing the optimal degree of stratification, and
smaller sample sizes will presumably warrant a different number of groups, but our
preliminary results here suggest that a range of strategies can yield significant
benefits over simple medians. 22
22 See Hansen et al (1953) and Everitt (1980) for more information on the theoretical issues in
the optimal grouping of data.
26
Figure 4: Geographic and Price-based Groupings
Deviation from trend, RMSE
%
●
%
Deviation of the median
4
4
Price-based grouping
3
3
SSD grouping
2
●
2
SLA grouping
●
1
1
0
0
0
10
20
30
40
Number of groups
Source:
Authors’ analysis using data from APM
6.
Conclusion
50
60
One of the problems inherent in measuring housing price growth is that the sample
of dwellings transacted in any period may be far from random and the
characteristics of the sample may change from period to period. As a result, simple
measures of growth in mean or median housing prices will reflect changes in the
composition of dwellings sold as well as pure price changes. In this paper, we have
proposed a simple non-regression-based measure of house price growth that
addresses the problem of compositional change by stratifying individual
transactions into different groups. Our measure differs from those commonly used
internationally in that we group small geographic regions (suburbs) according to
the long-term average price of dwellings in those regions, rather than simply
clustering smaller geographic regions into larger geographic regions. That is, our
method of stratification is specifically designed to control for what appears to be
the most important form of compositional change, namely changes in the
proportion of houses sold in higher- and lower-priced regions in any period.
27
We find that stratifying sales in this manner produces a mix-adjusted measure of
price growth that substantially improves upon standard unstratified median
measures. In particular, when compared with a median measure, our mix-adjusted
measure of price growth is considerably less volatile, is not subject to seasonality,
and performs better in real time with limited data samples. Our results suggest that
seasonal adjustment should be considered a ‘bare minimum’ response to such
compositional effects. However, house prices are not truly seasonal: seasonality in
median prices arises because of seasonality in the composition of transactions that
occur. Our measure improves significantly upon seasonally adjusted medians,
because we are also able to account for compositional effects that are non-seasonal
in nature. In addition, our mix-adjusted growth rate lines up quite closely with
more advanced regression-based measures of price growth. Overall, this indicates
that it is possible to develop computationally simple estimates of price growth that
control for compositional change.
Given the recent run-up in house prices in many other countries and the
macroeconomic effects associated with this, developments in house prices are now
of significant interest to policy-makers. Therefore, the methodology outlined in
this paper may be applicable for measuring price growth in a number of countries.
Furthermore, the stratification techniques contained in this paper have broader
applications than just the measurement of house prices. Many industry bodies, not
just in the housing industry, use simple means or medians as a summary measure
because they are simple to compute. However, if samples are not random,
compositional change may be a major issue. This paper shows that if a sample is
stratified appropriately (by the variable that is most related to what is obscuring the
underlying movements of interest) substantial benefits can be achieved over a
median measure.
28
Appendix A: Using the Information in Individual Strata – Assessing
the Strength of Intra- versus Inter-state Influences
Although the proposed new measure of price changes was designed to look at
house prices on an aggregate city-wide level, the price movements in the individual
strata may also be of interest in answering questions about the behaviour of house
prices in different segments of the market. Accordingly, we briefly consider the
extent to which price movements in a particular segment of a capital city market,
as proxied by the median price of each decile (quintile), are correlated with price
movements of other market segments. Since our strata are defined in terms of
average prices for suburbs, they correspond to economic segments (e.g. the ‘higher
end’ and the ‘lower end’ of the market) rather than regional segments (e.g. the
inner or outer suburbs).
The average correlation coefficient between year-ended price changes in strata
medians across capital cities is 0.52, compared with an average correlation
coefficient of 0.79 for strata medians within the same capital city. The first of these
numbers points to a reasonable amount of co-movement in housing price growth
across different cities, suggesting the existence of a national housing cycle. This is
not surprising given that state business cycles are highly correlated and the
presence of many common national influences. 23 However, within-city
correlations tend to be even higher. This suggests the existence of significant
regional effects within individual markets.
To more fully examine the relationship of price growth between different market
segments, we calculated the correlation coefficients between quarterly changes in
median price in the 65 different strata. Using the 2 080 different correlation
coefficients, we then estimated a regression to assess what factors are associated
with higher correlations between strata. This allows us to test for same-city versus
across-city effects in price growth. It also allows us to test if there is any tendency
for some degree of segmentation between the markets for houses and apartments
and if higher-price strata tend to be more correlated with other higher-price strata,
23 Norman and Walker (2004) find a significant degree of co-movement across state business
cycles, with the major source of cyclical fluctuations in state cycles arising from shocks that
are common to all states.
29
and vice versa. To test the latter effect, we define the economic ‘distance’ between
two strata as the absolute magnitude of the difference between the decile rankings
of two strata. For example, the distance variable between decile 6 in Sydney and
decile 8 in Perth would be 2. 24 If we find that strata which are economically
relatively ‘close’ to each other tend to have higher correlations, this might be
evidence for the existence of factors working on a national level that have
differential effects on the higher- and lower-end of the nationwide property market.
We obtain the following regression result:
corrxy = 0.40 + 0.21samecity − 0.02dist xy − 0.10diffdwelltype
(0.01) (0.01)
(0.00)
(0.01)
(A1)
2
Adjusted R =0.25
where: corrxy refers to the correlation coefficient between median quarterly price
movements in strata x and y (where x≠y); samecity is a dummy variable which is
equal to 1 if x and y are in the same city (and 0 otherwise); distxy refers to
‘economic distance’ between two strata, as defined above; and diffdwelltype is a
dummy variable taking the value of 1 if x and y refer to different types of
dwellings. Heteroskedasticity-consistent standard errors are shown in parentheses
below the parameter estimates. 25
The results are as expected. The significant constant term suggests a noticeable comovement in price growth across different segments of the national market, with
its value of 0.40 indicating the average correlation between quarterly price
movements in two strata that are in different cities, of the same dwelling type, and
in the same economic segments (zero distance). The most important variable for
explaining differences in the strength of correlations is whether or not the two
24 In the case of quintiles, we number quintiles by the midpoint of two corresponding deciles:
for example, quintile 1 is considered to be decile 1.5, quintile 2 would be 3.5 and so on.
25 For ease of understanding, we show results using ordinary least squares (OLS). OLS may not
be the most appropriate estimator for this equation, given that the dependent variable is
bounded by 1 and –1. However, similar results hold when we run the regression using the
Fisher z transformation which can be used to transform the correlation coefficients into
normally distributed variables. An additional economic problem may result because as the
2 080 observations come from only 65 data series, this may bias the standard errors
downwards.
30
strata are in the same city, with this variable explaining around half of the fit of
Equation (A1).
The results also show that price movements are less correlated the greater the
economic distance between the two strata. This provides evidence of socioeconomic factors on a national level that have different impacts on price growth in
higher- and lower-priced suburbs. In addition, the results show a higher correlation
in price movements within dwelling types as opposed to across dwelling types,
suggesting that there may be factors which tend to affect nationwide house prices
more than apartment prices, or vice versa. This could be additional evidence of
some type of common socio-economic effects, as household type tends to differ
across dwelling types. 26
Overall, the results suggest that there is a reasonably high degree of correlation in
movements in dwelling prices across segments of the Australian housing market,
especially in cases where there is a higher degree of similarity between two market
segments in terms of location, dwelling type and ‘economic background’.
26 In other work, we have also used Granger causality tests to look for the existence of any
systematic lead-lag relationship between the higher- and lower-priced segments of the market.
The results differ across cities, with some cities suggesting Granger causality from the high
end to the low end, other cities suggesting the opposite, and others suggesting either no
causality or causality running in both directions. Overall, it appears there is no systematic
lead-lag relationship; rather, there is a high degree of contemporaneous correlation between
price movements in the higher- and lower-priced segments in each city.
31
References
(ABS) Australian Bureau of Statistics (2005), ‘Renovating the established house
price index’, ABS Information Paper No 6417.0.
Bourassa SC, F Hamelink, M Hoesli and BD MacGregor (1999), ‘Defining
housing submarkets’, Journal of Housing Economics, 8(2), pp 160–183.
Briggs J and V Duoba (2000), ‘STRAT2D: optimal bi-variate stratification
system’, Statistics New Zealand Catalogue No 01.093.0000.
Case KE and RJ Shiller (1987), ‘Prices of single-family homes since 1970: new
indexes for four cities’, New England Economic Review, September/October,
pp 45–56.
Everitt B (1980), Cluster Analysis, 2nd edn, Social Science Research Council by
Heinemann Educational Books, Halstead Press, New York.
Goodman AC and TG Thibodeau (2003), ‘Housing market segmentation and
hedonic prediction accuracy’, Journal of Housing Economics, 12(3), pp 181–201.
Hansen J (2006), ‘Australian house prices: a comparison of hedonic and
repeat-sales measures’, Reserve Bank of Australia Research Discussion Paper
No 2006-03.
Hansen MH, WN Hurwitz and WG Madow (1953), Sample survey methods and
theory: Volume I, Wiley, New York.
Lavallée P (1988), ‘Two-way optimal stratification using dynamic programming’,
Proceedings of the Survey Methods Section, 11th edn, American Statistics
Association, Alexandria, pp 646–651.
McCarthy J and RW Peach (2004), ‘Are home prices the next “bubble”?’,
Federal Reserve Bank of New York Economic Policy Review, 10(3), pp 1–17.
32
Meese RA and NE Wallace (1997), ‘The construction of residential housing price
indices: a comparison of repeat-sales, hedonic-regression, and hybrid approaches’,
Journal of Real Estate Finance and Economics, 14(1–2), pp 51–73.
Norman D and T Walker (2004), ‘Co-movement of Australian state business
cycles’, Reserve Bank of Australia Research Discussion Paper No 2004-09.
(REINZ) Real Estate Institute of New Zealand (2005), ‘Higher end property
sales drive residential median up further’, REINZ News Release, 19 April.
Copyright and Disclaimer Notices
The following Copyright and Disclaimer Notices apply to data on dwelling prices
obtained from Australian Property Monitors (APM) and reported in this RDP.
Copyright
Copyright © 2004 Australian Property Monitors Pty Limited. The particular state and territory
governments hold copyright in the government-sourced data. Used with permission under
licence. No liability accepted.
Disclaimers
In compiling this information APM relies upon information supplied by a number of external
sources. The information is supplied on the basis that while APM believes that all the
information in it will be correct at the time of publication, it does not warrant its accuracy or
completeness.
Queensland: Underlying data for Queensland are copyrighted to State of Queensland for which
no responsibility is accepted.
South Australia: Copyright in this information belongs to the South Australian Government and
the South Australian Government does not accept any responsibility for the accuracy or
completeness of the information or its suitability for any purpose.
Victoria: Some underlying Victorian information is © State of Victoria (Department of
Sustainability and Environment). Accuracy not warranted. Use is on the basis that the State of
Victoria shall bear no responsibility or liability whatsoever for any errors, faults, defects or
omissions in that information.
Western Australia: Copyright – The State of Western Australia (DOLA), (2004). Licence No.
PA75-2003. Based on information provided with the permission of DOLA.
Australian Capital Territory: The ACT data are the property of the Australian Capital Territory.
No part of them may in any form or by any means (electronic, mechanical, microcopying,
photocopying, recording or otherwise) be reproduced, stored in a retrieval system or transmitted
without prior written permission. Enquiries should be directed to: The Executive Director, ACT
Planning and Land Management GPO Box 1908 CANBERRA ACT 2601.